Answers
Answer: [tex]x^{10}+10x^8y+40x^6y^2+80x^4y^3+80x^2y^4+32y^5[/tex]
Step-by-step explanation:
[tex]\mathrm{Apply\:binomial\:theorem}:\quad \left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i[/tex]
[tex]a=x^2,\:\:b=2y[/tex]
[tex]=\sum _{i=0}^5\binom{5}{i}\left(x^2\right)^{\left(5-i\right)}\left(2y\right)^i[/tex][tex]=\frac{5!}{0!\left(5-0\right)!}\left(x^2\right)^5\left(2y\right)^0+\frac{5!}{1!\left(5-1\right)!}\left(x^2\right)^4\left(2y\right)^1+\frac{5!}{2!\left(5-2\right)!}\left(x^2\right)^3\left(2y\right)^2+\frac{5!}{3!\left(5-3\right)!}\left(x^2\right)^2\left(2y\right)^3+\frac{5!}{4!\left(5-4\right)!}\left(x^2\right)^1\left(2y\right)^4+\frac{5!}{5!\left(5-5\right)!}\left(x^2\right)^0\left(2y\right)^5[/tex]
simplify all = [tex]x^{10}+10x^8y+40x^6y^2+80x^4y^3+80x^2y^4+32y^5[/tex]
Related Questions
Loretta earns $10 a week
and puts $7.50 a week
into savings account and spends
the rest. How much does she
spend in six weeks?
Answers
c(ge + p) = n +j
Solve for c: C=
Answers
Answer:
[tex]c(ge + p) = n + j \\ \\ \frac{c(ge + p)}{(ge + p)} = \frac{n + j}{(ge + p)} \\ \\ { \boxed{ \boxed{c = \frac{n + j}{ge + p} }}}[/tex]
There are 6 times as many dogs as cats . If the total number of dogs and cats is 21 , how many dogs are there?
Answers
Answer:
126 cats .................
126 dogs........
A nut-raisin mix costs $5.26 per pound. Rashid buys 15.5 pounds of the mix for a party. Rashid’s estimated cost of the nut-raisin mix is
Answers
$81.53 is the cost of nut-raisin mix
Explain why a set of points that defines a plane cannot be collinear
Answers
Answer:
Three non-collinear points determine a plane.
Step-by-step explanation:
This statement means that if you have three points not on one line, then only one specific plane can go through those points. The plane is determined by the three points because the points show you exactly where the plane is
The mean life time of sample of 100 fluorescent light bulbs produced by a company is computed to be 1570 hours with a standard deviation of 120 hours. The company claims that the average life of the bulbs produced by it is 1600 hours. Using the level of significance of 0.05, is the claim acceptable?
Answers
Answer:
The mean lifetime of a sample of 100 fluorescent light bulbs produced by a company is
The mean lifetime of a sample of 100 fluorescent light bulbs produced by a company is computed to be 1570 hours with a standard deviation of 120 hours.
Step-by-step explanation:
https://www.cs.bu.edu/faculty/snyder/cs237/Handouts%20and%20Web%20Documents/Handouts/PracticeProblemsHypothesisTesting.pdf
Have a bless day
PLS Help I Need this by today :)
Simplify the expression -11 -(-12)
Answers
Answer:
1
Step-by-step explanation:
-11-(-12) is just -11 plus 12 so 1 is your final answer because 2 negatives make a positive when multiplying.
Answer:
1
Step-by-step explanation:
Quintina decided to increase the deduction percentage of her federal income tax rate from 14% to 16%. Quintina’s gross pay per month is $2,100. Her deductions before the change are listed in the table.
Deduction
Dollar Amount
Federal Income Tax
$294
State Income Tax
$89
Social Security
$85
Medicare
$35
What is her new monthly net pay? Round your answer to the nearest dollar.
$1555
$1591
$1595
$1639
Mark this and return
Answers
Answer:
The monthly net pay is [tex]\$1555[/tex].
Step-by-step explanation:
Step 1 :
Quintina decided to increase the deduction percentage of her federal income tax rate from [tex]14\%[/tex] to [tex]16\%.[/tex]
Quintina gross pay per month is [tex]\$2,100[/tex]
[tex]16\%[/tex] is written in the decimal form.
[tex]=\frac{16}{100}[/tex]
[tex]=0.16[/tex]
Federal income tax
[tex]=0.16[/tex] × Gross pay
[tex]=0.156[/tex] × [tex]2100[/tex]
[tex]=336[/tex]
Step 2:
Monthly net pay = Gross pay- Federal income tax - State Income Tax – social Security- Medicare.
[tex]=2100-336-89-85-35[/tex]
[tex]=2100-545[/tex]
[tex]=\$1555[/tex]
Therefore, the monthly net pay is [tex]\$1555.[/tex]
Learn more about income tax, refer:
https://brainly.com/question/1601662Answer$1555
Step-by-step explanation:
72. Evaluate 5a + 3a2 when a = - 3
Answers
[tex]5a + 3 {a}^{2} \\ = 5( - 3) + 3( { - 3}^{2} ) \\ = - 15 + 3(9) \\ = - 15 + 27 \\ = 12[/tex]
I hope I helped you^_^
Answer:
12
Step-by-step explanation:
5a + 3a^2 when a = -3
~Substitute
5(-3) + 3(-3)^2
~Simplify
-15 + 3(9)
-15 + 27
12
Best of Luck!
WILL GIVE BRAINLEST
Slove f(9) if f(x)= -6x - 1
Show Step-by-Step pls.
Answers
Answer:
Use the given functions to set up and simplify −by−Step.
f(9)=−55
Re-order terms so constants are on the left
⋅9=−55
f⋅9=−55
9=−55
Divide both sides of the equation by the same term
Simplify
Solution
=−55/9
If the maximum score on a quiz is 120, is it possible to have a mean of 100 after the fifth quiz
Answers
Answer:
i dont think it is possible since you are losing percentage by the fifth time you are taking a quiz so if the max score is 120 it is not possible to still get 100 percent on the fifth try to will lose percent i think you can get 100 percent by the second or third try
Step-by-step explanation:
If the surface area of a cube is 384, what is the length of one of the sides of
the cube?
Answers
Answer:
S = 8
Each side of a face is 8 units.
Step-by-step explanation:
The surface area of the cube is 384 units.
One face of the cube has an area of s^2
A cube has 6 faces
6s^2 = 384 Divide by 6
s^2 = 384 / 6
s^2 = 64 Take the square root of both sides
sqrt(s^2) = sqrt(64)
s = 8
Answer:
8 units
Step-by-step explanation:
Area of 1 side = 384 ÷ 6 = 64 sq units
Length of 1 side = sq.rt. (64) = 8 units Answer
Could you help please i really dont get it
Answers
Answer:
[tex]3.4 \: apple \: pounds = 5.61 \: dollars \\ 1 \: apple \: pound = \{ \frac{(1 \times 5.61)}{3.4} \} \: dollars \\ \\ = { \boxed{ \boxed{1.65 \: dollars \: per \: pound}}}[/tex]
Answer:
1.65
Step-by-step explanation:
5.61/3.4=1.65
5) Simplify the expression (2x - 5y) + (x + y).
Answers
Answer:
3x - 4y
Step-by-step explanation:
(2x - 5y) + (x + y)
2x + -5y + x + y <--- Let's remove the parentheses
(2x + x) + (-5y + y) <--- Combine Like Terms
3x - 4y <--- Final Answer :)
Answer:
(2x *x) + (-5y + y)
[tex] {2}^{2} + - {5y}^{2} [/tex]
73. Find F when C = 30 degrees in the formula F=9/5c+32 degrees
Answers
Answer:
f = 86
Step-by-step explanation:
f = 9/5c + 32
~Substitute
f = 9/5(30) + 32
~Simplify
f = 54 + 32
f = 86
Best of Luck!
If U.S. $1 = 7.82 Hong Kong dollars, what is the value of 25 Hong Kong dollars in U.S. dollars?
Answers
Answer:
3.25
Step-by-step explanation:
1 hong kong dollar = 0.13 cents in us dollars
0.13x25=3.25
The value of 25 Hong Kong dollars in U.S dollar is $3.1969
Given that :
$1 = 7.82 Hong Kong dollars
Let the equivalent Number of U.S dollars = p
This means that :
$1 = 7.82 Hong Kong dollars
$1 = 7.82 Hong Kong dollars $p = 25
Cross multiply :
25 × 1 = 7.82 × p
25 = 7.82p
Divide both sides by 7.82
25 / 7.82 = p
p = $3.1969
Hence, 25 Hong Kong dollars is 3.1969 U.S dollars.
Learn more : https://brainly.com/question/18109354
Markes recipe for 24 cookies calls for 2½ cups of flour.How much flour will markes need to make 60 cookies?
Answers
Answer:
6 1/4 cups of flour
Step-by-step explanation:
24/2 = 12
2.5/2 = 1.25
12 x 5 = 60
1.25 x 5 = 6.25 cups
For every 24 cookies Markes needs 2.5 cups of flour. So, for 12 cookies he needs half of that which is 1.25 cups. 12 is a fifth of 60, so we multiply 1.25 by 5 which gives us 6.25 cups of flour. :D
Express 350 as a product of its product factors
Answers
Answer:
70
Step-by-step explanation:
The prime factors of 350 are 2,5,7. Therefore, the product of prime factors = 2×5×7=70
The conference will begin at 8:30 a.m. and will last 5 hours 45 minutes. What time will the conference be over?
Answers
Answer:
The conference will be over at 2:15 pm.
Step-by-step explanation:
solve for x. y = 1/3 (x + w)
Answers
3 • y = 3 • 1/3(x+w)
3y = x + w
Step 2: get the x by itself by subtracting away the w
3y - w = x + w - w
3y - w = x
You’ve got your answer.
A motorist drives on a state road to and from work each day and pays $3.50 on tolls one-way.
(a) Write a model for the cost for tolls C (in S) for x working days.
(b) The department of transportation has a prepaid toll program that discounts tolls for high-volume use. The motorist can buy a pass for $112 per month. How many working days are required for the motorist to save money by buying the pass?
The model for the tolls cost is C= ?
Answers
Answer:
Step-by-step explanation:
What operation on both sides of the equation 6x=42 isolates the variable on one side? There may be more than one correct answer.
A. Subtracting 6x
B. Adding 6
C. Dividing by 6x
D. Dividing by 6
E. Multiplying by 6
F. Multiplying by 1/6
G. Dividing by 42
Answers
Answers:
D. Dividing by 6
F. Multiplying by 1/6
Step-by-step explanation: Dividing both sides by 6 and Multiplying by 1/6 will isolate the variable on one side because we will get the value of what x is equal too. X is equal to 7.
Answer:
D,E,F,G
Step-by-step explanation:
Find the Least Common Multiple (LCM) of 50 and 90
Answers
Answer:
450
(I can't post the answer if it's less than 20 letters so just ignore this I'm trying to fill up)
In exercises 1-2, solve the formula for the indicated variable.
1: Surface area of a cylinder: S=2πr^2+2πrh: Solve for h.
2: Area of a trapezoid: A=1/2h(b1 + b2); Solve for b2.
The 1 and 2 are supposed to be under to the side of b like this.
Answers
Answer:
area of a trapezoid A =1Step-by-step explanation:
2
Which expression is equivalent to (3−22)+5?
All the Second 2s are exponent
5−22
22−5
5−32
32−5
Answers
Answer:
3²-5
Step-by-step explanation:
(3-2²)+5=4
3²-5=4
Answer:
D
Step-by-step explanation:
First off, lets simplify (3-2^2)+5 = -1+5 = 4
We will need to find an expression that will equal to 4
lets try 1, 5-2^2 = 1, 1 =\ 4
Alright, lets try 2, 2^2 -5 = -1, -1=\5
Now lets try 3, 5 - 3^2 = -4, -4=\4
So by process of elimination we can say that D is correct by I will show you why it is correct. 3^2 -5 = 4, 4=4
If you have any questions ask me.
Hope it helped :)
What is the least common denominator for the fractions 1/2 and 3/8
Answers
Answer:
LCD = 8
Step-by-step explanation:
All you have to do is times both the denominator and numerator of 1/2 by 4.
So 1 times 4 = 4 and 2 times 4 is 8.
4/8 and 3/8
How to solve -3/9 + ( -2 9/10)
[tex] - 3 \sqrt{8 + ( - 2 \times \frac{9}{10} } [/tex]
Answers
9514 1404 393
Answer:
-3 7/30-7.46994Step-by-step explanation:
We understand this to be two separate problems.
-3/9 +(-2 9/10) = -(3/9 +2 9/10)
= -(10/30 +87/30) = -97/30 = -3 7/30
__
-3√(8 +(-2(9/10))) = -3√(8 -1.8) = -3√6.2 ≈ -7.46994
__
Additional comment
A calculator can help with these, especially if it is able to deal with rational numbers. (Many graphing calculators and some scientific calculators will do that more or less nicely. My favorite Android calculator app makes arithmetic with fractions and mixed numbers very easy.)
We're planning to enclose a rectangular field with fencing, and we know that for whatever reason we want the field to be 50 feet square. We also know that the field's width should be 23 feet longer than the field's length. What are the field's dimensions?
Answers
Answer:
[tex]? \times \frac{?}{?} [/tex]
d
Answer:
2 by 25 feet.
Step-by-step explanation:
Let L and W be the length and the widht of the field
we want W = L + 23 and W x L = 50
So
(L + 23) x L = 50
[tex]L^2 + 23L = 50\\L^2+23L-50 =0\\(L+25)(L-2)=0\\L=-25 \text{ or } L = 2[/tex]
Since L must be positive then L =2 and W = 2 + 23 = 25.
A park ranger hiked 3/4 mi to a lookout, another 5/7 mi to a bird's nest, and finally 5/14 mi to a campsite. How far did the park ranger hike?
Answers
Answer:
2 miles and 88 yards.
Step-by-step explanation:
4 has 2*2 as prime factors
5 is prime
10 has 2 and 5 as prime factors
Thus, the lowest common denominator will be 2*2*5
3/4=15/20
3/5=12/20
7/10=14/20
Now that we have three fractions with the same denominator, we can add the numerators
15+12+14=41
So 41/20ths
That’s 2 and 1/20th
So the final answer is 2 miles and 88 yards! :)
(01.01 LC)An athlete took forward and backward steps of equal distance to warm up before his race. After taking 10 steps total, he was back at his starting position. How many steps did the athlete take in the forward and backward directions?
I would love the help.
Answers
9514 1404 393
Answer:
5 steps forward5 steps backwardStep-by-step explanation:
In order for the total displacement to be zero, the amount of forward displacement must be equal and opposite to the amount of backward displacement. Since the steps are the same length, they must be equal in number.
Half of the 10 steps were forward, and the other half were backward.
5 steps forward; 5 steps backward.
_____
Additional comment
Math develops from an effort to model the real world. It would probably give you some insight into this problem if you were to physically take some steps to see how many forward and backward you would need to end where you start.
